Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#19104733 | C2 | semidirect |
| 5. #23781874 | C2 | semidirect |
| 6. #23781869 | C2 | semidirect |
| 7. #23781688 | C2 | semidirect |
| 8. #23781673 | C2 | semidirect |
| 9. #419×C163 | C2 | semidirect |
| 116. Dic163 | #137 | semidirect |
| 121. C163 | #3039 | semidirect |
| 131. #419 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104768 | 2 |
| C2×#19104766 | 2 |
| C2×#19104733 | 2 |
| #23782133 | 2 |
| #23781874 | 2 |
| #23781869 | 2 |
| #23781688 | 2 |
| #23781673 | 2 |
| #419×C163 | 2 |
| #3039 | 163 |